To answer the question:

1. She didn't know she was going to die on that bed.
2. She was asked to tell the story to researchers wanting to find a jewel.
3. She got caught up in her story.

Perfectly normal.

Now for what is not normal is that Rose is extremely coldhearted and selfish throughout the entire story, even when she's telling the story from her perspective and one of her only redeeming qualities that she has is that she's not Cal. But remember, this is HER version of the story. Imagine how the perspectives could have been wildly different from hers.
Anyway in HER version of the story..:

1. Rose denies her husband and children her wealth.
   She never told anyone about it and throws away the jewel
   that could have been extremely useful for her children or grandchildren.
   Their tuition, medical expenses, you name it.
   Not to mention it would have given the researchers
   closure to all of their efforts to find this treasure,
   which we now know will be fruitless.
   And she's did it with glee, saying "Oops" with a smile.
   Oh yeah, spite those researchers and your children granny!
   We've really seen how awful they are, especially her children.
   And if she hated her own children, she could have given the money to charity.
   Or she could have given it to Jack's family. But I guess the family of a hobo
   would never appreciate such a gift.
2. Rose killed Jack.
   She never regretted having hogged the wreckage that could have saved Jack's life.
   Mythbusters proved that the life vests could have been used to give the wreckage more
   bouyancy that would have kept them both afloat.
   They could have taken turns on that wreckage. She could have given him her life vest.
   She could have stayed on the life boats, then Jack would have had the wreckage on his own.
   She could have traded herself in for Jack since she was the idiot having made the dumb decision of leaving the lifeboat.
   Jack died through her actions and for 70 years until her death this never occured to her.
   Not to mention, since she went on the life boat, she's responsible for taking a seat that could have been taken by another person. A child, a man, a lady. That person would have survived.
   Or it could have been her maid Trudy, who died on the ship because there wasn't enough space on the life boats.
3. Rose flips on her secret lover When Jack is being framed by her fiancée of being a thief,
   she lets him down by believing her fiancée's lies,
   despite her telling Jack that she trusts him.
   I guess not.
   This almost gets Jack killed at an earlier time.
4. Rose knows that through her cheating, she is accidentally responsible for every single one of those deaths of that happened on the Titanic, including children and babies and doesn't regret that at all.
   She could have felt guilt for not communicating clearly to Cal that this isn't working out.
   That she made a mistake by going on board with this ship.
   But instead she secretly runs off, kisses Jack on deck, which distracts of couple of crew members that were specifically there to watch the sea for icebergs. She could have felt guilty for not having kissed in a more more private area.
   She could have felt guilty for cheating in the first place.
   And when her fiancée finds out that she's cheating with him, she just reacts coldly towards him, to which he flips the table in rage and slaps her... in HER version of the story.
5. She doesn't let her mother know that she's alive.
   She lets no one know that she's alive after the Titanic sunk. That includes her own mother.
   Instead she takes up the last name of the man she killed. Creepy.
   Speaking of her mother,
   when Rose lights up a cigarette and blows smoke close to her mother's face, her mother asks Rose to please stop doing that, you know I don't like that,
   She then responds to fully blowing smoke into her mother's face.
   Disrespectful.
6. Her last thoughts before she dies are of her dancing with Jack.
   Not of her husband she lived 70 years with.
   Not of her children, not of her grandchildren.
   Just a hobo she had a fling with for two days... that she killed... among a thousand others.
   And she doesn't think of her husband and children and grandchildren during those last,
   she doesn't think of them during the entire movie. Never. Not once do we see them.
   What we do see are eight pictures on her nightstand. Every single one of them are of herself.
   Herself.

Now I said 'one of her few redeeming qualities' because she another one.
That is that she was 17 at the time,
and being played by a 20 year old Kate Winslet that's a bit difficult to see.
However, even 17 year olds would be more responsible as she acts like a 13 year old,
since that's what her character is actually based on, 13-year old Juliet from Romeo and Juliet.
But as much as this would have redeemed Rose's actions on the boat as a teenager,
those reflections should have hit the Rose the grandma to put things into perspective.
That didn't happen.